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What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=x+2g(x) = x + 2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______

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Q. What is (f∗g)(x)(f * g)(x)?\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=x+2g(x) = x + 2\newlineWrite your answer as a polynomial or a rational function in simplest form.\newline______
  1. Identify formula: Identify the formula for (f∗g)(x)(f * g)(x).(f∗g)(x)(f * g)(x) is the product of f(x)f(x) and g(x)g(x).(f∗g)(x)=f(x)∗g(x)(f * g)(x) = f(x) * g(x)
  2. Define functions: We have:\newlinef(x)=−x2f(x) = -x^2\newlineg(x)=x+2g(x) = x + 2\newlineNow, we need to multiply these two functions to find (f∗g)(x)(f * g)(x).\newline(f∗g)(x)=(−x2)∗(x+2)(f * g)(x) = (-x^2) * (x + 2)
  3. Multiply functions: Distribute −x2-x^2 to both terms in the parentheses.\newline(f∗g)(x)=(−x2∗x)+(−x2∗2)(f * g)(x) = (-x^2 * x) + (-x^2 * 2)
  4. Distribute terms: Simplify the expression by multiplying the terms.\newline(f⋅g)(x)=−x3−2x2(f \cdot g)(x) = -x^3 - 2x^2

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